Sensitivity Analysis in an Immuno-Epidemiological Vector-Host Model.

Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development. Thus the value of understanding the impact of immunological parameters on epidemiological quantities. Here we consider an age-since-infection structured vector-host model, in which epidemiological parameters are formulated as functions of within-host virus and antibody densities, governed by an ODE system. We then use SA for these immuno-epidemiological models to investigate the impact of immunological parameters on population-level disease dynamics such as basic reproduction number, final size of the epidemic or the infectiousness at different phases of an outbreak. As a case study, we consider Rift Valley Fever Disease utilizing parameter estimations from prior studies. SA indicates that [Formula: see text] increase in within-host pathogen growth rate can lead up to [Formula: see text] increase in [Formula: see text] up to [Formula: see text] increase in steady-state infected host abundance, and up to [Formula: see text] increase in infectiousness of hosts when the reproduction number [Formula: see text] is larger than one. These significant increases in population-scale disease quantities suggest that control strategies that reduce the within-host pathogen growth can be important in reducing disease prevalence.

A structured population model with diffusion in structure space.

A structured population model is described and analyzed, in which individual dynamics is stochastic. The model consists of a PDE of advection-diffusion type in the structure variable. The population may represent, for example, the density of infected individuals structured by pathogen density x, [Formula: see text]. The individuals with density [Formula: see text] are not infected, but rather susceptible or recovered. Their dynamics is described by an ODE with a source term that is the exact flux from the diffusion and advection as [Formula: see text]. Infection/reinfection is then modeled moving a fraction of these individuals into the infected class by distributing them in the structure variable through a probability density function. Existence of a global-in-time solution is proven, as well as a classical bifurcation result about equilibrium solutions: a net reproduction number [Formula: see text] is defined that separates the case of only the trivial equilibrium existing when [Formula: see text] from the existence of another-nontrivial-equilibrium when [Formula: see text]. Numerical simulation results are provided to show the stabilization towards the positive equilibrium when [Formula: see text] and towards the trivial one when [Formula: see text], result that is not proven analytically. Simulations are also provided to show the Allee effect that helps boost population sizes at low densities.

Sexually transmitted infections and dating app use.

Incidence of sexually transmitted infections (STIs) is rising sharply in the United States. Between 2014 and 2019, incidence among men and women has increased by 62.8% and 21.4%, respectively, with an estimated 68 million Americans contracting an STI in 2018.a Some human behaviors impacting the expanding STI epidemic are unprotected sex and multiple sexual partners.b Increasing dating app usage has been postulated as a driver for increases in the numbers of people engaging in these behaviors. Using the proposed model, it is estimated that both STI incidence and prevalence for females and males have increased annually by 9%-15% between 2015 and 2019 due to dating apps usage, and that STI incidence and prevalence will continue to increase in the future. The model is also used to assess the possible benefit of in-app prevention campaigns.ahttps://www.cdc.gov/nchhstp/newsroom/fact-sheets/std/STI-Incidence-Prevalence-Cost-Factsheet.htmbA. N. Sawyer, E. R. Smith, and E. G. Benotsch. Dating application use and sexual risk behavior among young adults. Sexuality Research and Social Policy, 15:183-191, 2018.

Mechanistic modeling of alarm signaling in seed-harvester ants.

Ant colonies demonstrate a finely tuned alarm response to potential threats, offering a uniquely manageable empirical setting for exploring adaptive information diffusion within groups. To effectively address potential dangers, a social group must swiftly communicate the threat throughout the collective while conserving energy in the event that the threat is unfounded. Through a combination of modeling, simulation, and empirical observations of alarm spread and damping patterns, we identified the behavioral rules governing this adaptive response. Experimental trials involving alarmed ant workers (Pogonomyrmex californicus) released into a tranquil group of nestmates revealed a consistent pattern of rapid alarm propagation followed by a comparatively extended decay period [1]. The experiments in [1] showed that individual ants exhibiting alarm behavior increased their movement speed, with variations in response to alarm stimuli, particularly during the peak of the reaction. We used the data in [1] to investigate whether these observed characteristics alone could account for the swift mobility increase and gradual decay of alarm excitement. Our self-propelled particle model incorporated a switch-like mechanism for ants' response to alarm signals and individual variations in the intensity of speed increased after encountering these signals. This study aligned with the established hypothesis that individual ants possess cognitive abilities to process and disseminate information, contributing to collective cognition within the colony (see [2] and the references therein). The elements examined in this research support this hypothesis by reproducing statistical features of the empirical speed distribution across various parameter values.

The role of sexually abstained groups in two-sex demographic and epidemic logistic models with non-linear mortality.

We describe several gender structured population models governed by logistic growth with non-linear death rate. We extend these models to include groups of people isolated from sexual activity and individuals exposed to a mild and long-lasting sexually transmitted disease, i.e. without disease-induced mortality and recovery. The transmission of the disease is modeled through formation/separation of heterosexual couples assuming that one infected individual automatically infects his/her partner. We are interested in how the non-reproductive class may change the demographic tendencies in the general population and whether they can curb the growth of the infected group while keeping the healthy one at acceptable levels. A comparison of the equilibrium total population size in the presence and the absence of the isolated class is also provided.

An SEIQR model for childhood diseases.

It has been shown that the inclusion of an isolated class in the classical SIR model for childhood diseases can be responsible for self-sustained oscillations. Hence, the recurrent outbreaks of such diseases can be caused by autonomous, deterministic factors. We extend the model to include a latent class (i.e. individuals who are infected with the disease, but are not yet able to pass the disease to others) and study the resulting dynamics. The existence of Hopf bifurcations is shown for the model, as well as a homoclinic bifurcation for a perturbation to the model. For historical data on scarlet fever in England, our model agrees with the epidemiological data much more closely than the model without the latent class. For other childhood diseases, our model suggests that isolation is unlikely to be a major factor in sustained oscillations.

A Mathematical model of Schistosoma mansoni in Biomphalaria glabrata with control strategies.

We describe and analyze a mathematical model for schistosomiasis in which infected snails are distinguished from susceptible through increased mortality and no reproduction. We based the model on the same derivation as Anderson and May (J. Anim. Ecol. 47:219-247, 1978), Feng and Milner (A New Mathematical Model of Schistosomiasis, Mathematical Models in Medical and Health Science, Nashville, TN, 1997. Innov. Appl. Math., Vanderbilt Univ. Press, Nashville, pp. 117-128, 1998), and May and Anderson (J. Anim. Ecol. 47:249-267, 1978), but used logistic growth both in human and snail hosts. We introduce a parameter r, the effective coverage of medical treatment/prevention to control the infection. We determine a reproductive number for the disease directly related to its persistence and extinction. Finally, we obtain a critical value for r that indicates the minimum treatment effort needed in order to clear out the disease from the population.

Sex-biased prevalence in infections with heterosexual, direct, and vector-mediated transmission: A theoretical analysis.

Three deterministic Kermack-McKendrick-type models for studying the transmission dynamics of an infection in a two-sex closed population are analyzed here. In each model it is assumed that infection can be transmitted through heterosexual contacts, and that there is a higher probability of transmission from one sex to the other than vice versa. The study is focused on understanding whether and how this bias in transmission reflects in sex differences in final attack ratios (i.e. the fraction of individuals of each sex that eventually gets infected). In the first model, where the other two transmission modes are not considered, the attack ratios (fractions of the population of each sex that will eventually be infected) can be obtained as solutions of a system of two nonlinear equations, that has a unique solution if the net reproduction number exceeds unity. It is also shown that the ratio of attack ratios depends solely on the ratio of gender-specific susceptibilities and on the basic reproductive number of the epidemic Ro, and that the gender-specific final attack-ratio is biased in the same direction as the gender-specific susceptibilities. The second model allows also for infection transmission through direct, non-sexual, contacts. In this case too, an analytical expression is derived from which the attack ratios can be obtained. The qualitative results are similar to those obtained for the previous model, but another important parameter for determining the value of the ratio between the attack ratios in the two sexes is obtained, the relative weight of direct vs. heterosexual transmission (namely, ρ). Quantitatively, the ratio of final attack ratios generally will not exceed 1.5, if non-sexual transmission accounts for most transmission events (ρ≥0.6) and the ratio of gender-specific susceptibilities is not too large (say, 5 at most). The third model considers vector-borne, instead of direct transmission. In this case, we were not able to find an analytical expression for the final attack ratios, but used instead numerical simulations. The results on final attack ratios are actually quite similar to those obtained with the second model. It is interesting to note that transient patterns can differ from final attack ratios, as new cases will tend to occur more often in the more susceptible sex, while later depletion of susceptibles may bias the ratio in the opposite direction. The analysis of these simple models, despite their lack of realism, can help in providing insight into, and assessment of, the potential role of gender-specific transmission in infections with multiple modes of transmission, such as Zika virus (ZIKV), by gauging what can be expected to be seen from epidemiological reports of new cases, disease incidence and seroprevalence surveys.

A schistosomiasis model with an age-structure in human hosts and its application to treatment strategies.

We study a system of partial differential equations which models the disease transmission dynamics of schistosomiasis. The model incorporates both the definitive human hosts and the intermediate snail hosts. The human hosts have an age-dependent infection rate and the snail hosts have an infection-age-dependent cercaria releasing rate. The parasite reproduction number R is computed and is shown to determine the disease dynamics. Stability results are obtained via both analytic and numerical studies. Results of the model are used to discuss age-targeted drug treatment strategies for humans. Sensitivity and uncertainty analysis is conducted to determine the role of various parameters on the variation of R. The effects of various drug treatment programs on disease control are compared in terms of both R and the mean parasite load within the human hosts.

The application of an age-structured model with unbounded mortality to demography.

We carry out a simulation of the female population of the USA using the non-autonomous Lotka-McKendrick model with finite maximum age and recent demographic data. The most important contributions in our study are the identification of the mortality rate (including the maximum age) and the design and analysis of a numerical method that works efficiently with unbounded mortality rates. We also consider the effect in the population projections produced by different ways to choose the vital rates and we present a sensitivity analysis with respect to the mortality. Finally, we exemplify the limitations the data impose on the quality of the projections of this model through a 10-year simulation for the USA from 1990 to 2000 and we project the female population of the USA in 2010 using this model.

Schistosomiasis models with density dependence and age of infection in snail dynamics.

New models for schistosomiasis are developed. These models incorporate several realistic features including drug treatment for human hosts, an infection age in snail hosts, density-dependent birth rate of snails, distribution of schistosomes within human hosts, and disease-induced mortality in both human and snail hosts. The qualitative and quantitative mathematical properties of the models are studied, their biological consequences and some control strategies are discussed, and the results of the new models are compared with those of simpler models. It is shown that the new model may have a bifurcation at which the unique endemic equilibrium changes the stability and stable periodic solutions exist. This is quite different from the simpler models. Explicit thresholds of treatment rate are established above which the infection will be controlled under certain levels. Evaluations of cost-effectiveness are also discussed by analyzing the sensitivity of the mean number of parasites per person to changes of other parameters.

The logistic, two-sex, age-structured population model.

In this paper, we introduce the logistic effect into the two-sex population model introduced by Hoppensteadt. We address the problem of existence and uniqueness of continuous and classical solutions. We first give sufficient conditions for a unique continuous solution to exist locally and also globally. Next, the existence of classical solutions is established under some mild assumptions on the vital rates. Finally, we study the existence of equilibria and give an upper bound for the total population at steady state.

A deterministic model of schistosomiasis with spatial structure.

It has been observed in several settings that schistosomiasis is less prevalent in segments of river with fast current than in those with slow current. Some believe that this can be attributed to flush-away of intermediate host snails. However, free-swimming parasite larvae are very active in searching for suitable hosts, which indicates that the flush-away of larvae may also be very important. In this paper, the authors establish a model with spatial structure that characterizes the density change of parasites following the flush-away of larvae. It is shown that the reproductive number, which is an indicator of prevalence of parasitism, is a decreasing function of the river current velocity. Moreover, numerical simulations suggest that the mean parasite load is low when the velocity of river current flow is sufficiently high.

The effect of nonreproductive groups on persistent sexually transmitted diseases.

We describe several population models exposed to a mild life long sexually transmitted disease, i.e. without significant increased mortality among infected individuals and providing no immunity/recovery. We then modify these models to include groups isolated from sexual contact and analyze their potential effect on the dynamics of the population. We are interested in how the isolated class may curb the growth of the infected group while keeping the healthy population at acceptable levels.

How do nonreproductive groups affect population growth?

I describe several models of population dynamics, both unstructured and gender structured, that include groups of individuals who do not reproduce. I analyze the effect that the nonreproductive group may have on the dynamics of the whole population in terms of the vital rates and the proportion of nonreproductive individuals, and we provide specific examples for real populations.